Nodal minimal partitions in dimension $3$
Bernard Helffer Thomas Hoffmann-Ostenhof Susanna Terracini
Discrete & Continuous Dynamical Systems - A 2010, 28(2): 617-635 doi: 10.3934/dcds.2010.28.617
In continuation of [20], we analyze the properties of spectral minimal $k$-partitions of an open set $\Omega$ in $\mathbb R^3$ which are nodal, i.e. produced by the nodal domains of an eigenfunction of the Dirichlet Laplacian in $\Omega$. We show that such a partition is necessarily a nodal partition associated with a $k$-th eigenfunction. Hence we have in this case equality in Courant's nodal theorem.
keywords: Optimal partitions; Eigenvalues; Nodal domains; Courant nodal Theorem; Spectral minimal partitions.

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